%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC038+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 22:28:59 EDT 2022 % Result : Theorem 30.96s 31.16s % Output : Proof 30.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWC038+1 : TPTP v8.1.0. Released v2.4.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.14/0.33 % Computer : n026.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 600 % 0.14/0.33 % DateTime : Sun Jun 12 03:50:50 EDT 2022 % 0.14/0.34 % CPUTime : % 30.96/31.16 (* PROOF-FOUND *) % 30.96/31.16 % SZS status Theorem % 30.96/31.16 (* BEGIN-PROOF *) % 30.96/31.16 % SZS output start Proof % 30.96/31.16 Theorem co1 : (forall U : zenon_U, ((ssList U)->(forall V : zenon_U, ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = V))\/((~(V = X))\/((~(U = W))\/(((nil) = U)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))))))). % 30.96/31.16 Proof. % 30.96/31.16 assert (zenon_L1_ : (~((nil) = (nil))) -> False). % 30.96/31.16 do 0 intro. intros zenon_H60. % 30.96/31.16 apply zenon_H60. apply refl_equal. % 30.96/31.16 (* end of lemma zenon_L1_ *) % 30.96/31.16 assert (zenon_L2_ : forall (zenon_TX_dv : zenon_U), (ssList zenon_TX_dv) -> (~(frontsegP zenon_TX_dv (nil))) -> False). % 30.96/31.16 do 1 intro. intros zenon_H61 zenon_H62. % 30.96/31.16 generalize (ax45 zenon_TX_dv). zenon_intro zenon_H64. % 30.96/31.16 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 30.96/31.16 exact (zenon_H66 zenon_H61). % 30.96/31.16 exact (zenon_H62 zenon_H65). % 30.96/31.16 (* end of lemma zenon_L2_ *) % 30.96/31.16 assert (zenon_L3_ : forall (zenon_TX_dv : zenon_U), (ssList zenon_TX_dv) -> (~(frontsegP (nil) zenon_TX_dv)) -> ((nil) = zenon_TX_dv) -> False). % 30.96/31.16 do 1 intro. intros zenon_H61 zenon_H67 zenon_H68. % 30.96/31.16 generalize (ax46 zenon_TX_dv). zenon_intro zenon_H69. % 30.96/31.16 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H66 | zenon_intro zenon_H6a ]. % 30.96/31.16 exact (zenon_H66 zenon_H61). % 30.96/31.16 apply (zenon_equiv_s _ _ zenon_H6a); [ zenon_intro zenon_H67; zenon_intro zenon_H6c | zenon_intro zenon_H6b; zenon_intro zenon_H68 ]. % 30.96/31.16 exact (zenon_H6c zenon_H68). % 30.96/31.16 exact (zenon_H67 zenon_H6b). % 30.96/31.16 (* end of lemma zenon_L3_ *) % 30.96/31.16 assert (zenon_L4_ : forall (zenon_TX_dv : zenon_U) (zenon_TW_ei : zenon_U) (zenon_TV_ej : zenon_U), (~(zenon_TV_ej = zenon_TW_ei)) -> (zenon_TV_ej = zenon_TX_dv) -> (zenon_TW_ei = zenon_TX_dv) -> False). % 30.96/31.16 do 3 intro. intros zenon_H6d zenon_H6e zenon_H6f. % 30.96/31.16 cut ((zenon_TV_ej = zenon_TX_dv) = (zenon_TV_ej = zenon_TW_ei)). % 30.96/31.16 intro zenon_D_pnotp. % 30.96/31.16 apply zenon_H6d. % 30.96/31.16 rewrite <- zenon_D_pnotp. % 30.96/31.16 exact zenon_H6e. % 30.96/31.16 cut ((zenon_TX_dv = zenon_TW_ei)); [idtac | apply NNPP; zenon_intro zenon_H72]. % 30.96/31.16 cut ((zenon_TV_ej = zenon_TV_ej)); [idtac | apply NNPP; zenon_intro zenon_H73]. % 30.96/31.16 congruence. % 30.96/31.16 apply zenon_H73. apply refl_equal. % 30.96/31.16 apply zenon_H72. apply sym_equal. exact zenon_H6f. % 30.96/31.16 (* end of lemma zenon_L4_ *) % 30.96/31.16 assert (zenon_L5_ : forall (zenon_TV_ej : zenon_U) (zenon_TX_dv : zenon_U) (zenon_TW_ei : zenon_U), (forall V : zenon_U, ((ssList V)->(((frontsegP zenon_TW_ei V)/\(frontsegP V zenon_TW_ei))->(zenon_TW_ei = V)))) -> (ssList zenon_TX_dv) -> (ssList zenon_TW_ei) -> (zenon_TX_dv = (nil)) -> (frontsegP zenon_TX_dv zenon_TW_ei) -> (~(zenon_TV_ej = zenon_TW_ei)) -> (zenon_TV_ej = zenon_TX_dv) -> False). % 30.96/31.16 do 3 intro. intros zenon_H74 zenon_H61 zenon_H75 zenon_H76 zenon_H77 zenon_H6d zenon_H6e. % 30.96/31.16 generalize (zenon_H74 zenon_TX_dv). zenon_intro zenon_H78. % 30.96/31.16 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H66 | zenon_intro zenon_H79 ]. % 30.96/31.16 exact (zenon_H66 zenon_H61). % 30.96/31.16 apply (zenon_imply_s _ _ zenon_H79); [ zenon_intro zenon_H7a | zenon_intro zenon_H6f ]. % 30.96/31.16 apply (zenon_notand_s _ _ zenon_H7a); [ zenon_intro zenon_H7c | zenon_intro zenon_H7b ]. % 30.96/31.16 generalize (ax40 zenon_TW_ei). zenon_intro zenon_H7d. % 30.96/31.16 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 30.96/31.16 exact (zenon_H7f zenon_H75). % 30.96/31.16 generalize (zenon_H7e (nil)). zenon_intro zenon_H80. % 30.96/31.16 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H82 | zenon_intro zenon_H81 ]. % 30.96/31.16 exact (zenon_H82 ax17). % 30.96/31.16 generalize (zenon_H81 zenon_TX_dv). zenon_intro zenon_H83. % 30.96/31.16 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H66 | zenon_intro zenon_H84 ]. % 30.96/31.16 exact (zenon_H66 zenon_H61). % 30.96/31.16 apply (zenon_imply_s _ _ zenon_H84); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 30.96/31.16 apply (zenon_notand_s _ _ zenon_H86); [ zenon_intro zenon_H87 | zenon_intro zenon_H67 ]. % 30.96/31.16 generalize (ax45 zenon_TW_ei). zenon_intro zenon_H88. % 30.96/31.16 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H7f | zenon_intro zenon_H89 ]. % 30.96/31.16 exact (zenon_H7f zenon_H75). % 30.96/31.16 exact (zenon_H87 zenon_H89). % 30.96/31.16 generalize (ax46 zenon_TX_dv). zenon_intro zenon_H69. % 30.96/31.16 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H66 | zenon_intro zenon_H6a ]. % 30.96/31.16 exact (zenon_H66 zenon_H61). % 30.96/31.16 apply (zenon_equiv_s _ _ zenon_H6a); [ zenon_intro zenon_H67; zenon_intro zenon_H6c | zenon_intro zenon_H6b; zenon_intro zenon_H68 ]. % 30.96/31.16 apply zenon_H6c. apply sym_equal. exact zenon_H76. % 30.96/31.16 exact (zenon_H67 zenon_H6b). % 30.96/31.16 exact (zenon_H7c zenon_H85). % 30.96/31.16 exact (zenon_H7b zenon_H77). % 30.96/31.16 apply (zenon_L4_ zenon_TX_dv zenon_TW_ei zenon_TV_ej); trivial. % 30.96/31.16 (* end of lemma zenon_L5_ *) % 30.96/31.16 apply NNPP. intro zenon_G. % 30.96/31.16 apply (zenon_notallex_s (fun U : zenon_U => ((ssList U)->(forall V : zenon_U, ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = V))\/((~(V = X))\/((~(U = W))\/(((nil) = U)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))))))) zenon_G); [ zenon_intro zenon_H8a; idtac ]. % 30.96/31.16 elim zenon_H8a. zenon_intro zenon_TU_fj. zenon_intro zenon_H8c. % 30.96/31.16 apply (zenon_notimply_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 30.96/31.16 apply (zenon_notallex_s (fun V : zenon_U => ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = V))\/((~(V = X))\/((~(zenon_TU_fj = W))\/(((nil) = zenon_TU_fj)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))))) zenon_H8d); [ zenon_intro zenon_H8f; idtac ]. % 30.96/31.16 elim zenon_H8f. zenon_intro zenon_TV_ej. zenon_intro zenon_H90. % 30.96/31.16 apply (zenon_notimply_s _ _ zenon_H90). zenon_intro zenon_H92. zenon_intro zenon_H91. % 30.96/31.16 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = zenon_TV_ej))\/((~(zenon_TV_ej = X))\/((~(zenon_TU_fj = W))\/(((nil) = zenon_TU_fj)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))) zenon_H91); [ zenon_intro zenon_H93; idtac ]. % 30.96/31.16 elim zenon_H93. zenon_intro zenon_TW_ei. zenon_intro zenon_H94. % 30.96/31.16 apply (zenon_notimply_s _ _ zenon_H94). zenon_intro zenon_H75. zenon_intro zenon_H95. % 30.96/31.16 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~((nil) = zenon_TV_ej))\/((~(zenon_TV_ej = X))\/((~(zenon_TU_fj = zenon_TW_ei))\/(((nil) = zenon_TU_fj)\/(((~((nil) = X))\/(~((nil) = zenon_TW_ei)))/\((~(neq zenon_TW_ei (nil)))\/(~(frontsegP X zenon_TW_ei)))))))))) zenon_H95); [ zenon_intro zenon_H96; idtac ]. % 30.96/31.16 elim zenon_H96. zenon_intro zenon_TX_dv. zenon_intro zenon_H97. % 30.96/31.16 apply (zenon_notimply_s _ _ zenon_H97). zenon_intro zenon_H61. zenon_intro zenon_H98. % 30.96/31.16 apply (zenon_notor_s _ _ zenon_H98). zenon_intro zenon_H9a. zenon_intro zenon_H99. % 30.96/31.16 apply (zenon_notor_s _ _ zenon_H99). zenon_intro zenon_H9c. zenon_intro zenon_H9b. % 30.96/31.16 apply (zenon_notor_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 30.96/31.16 apply (zenon_notor_s _ _ zenon_H9d). zenon_intro zenon_Ha0. zenon_intro zenon_H9f. % 30.96/31.16 apply zenon_H9e. zenon_intro zenon_Ha1. % 30.96/31.16 apply zenon_H9c. zenon_intro zenon_H6e. % 30.96/31.16 apply zenon_H9a. zenon_intro zenon_Ha2. % 30.96/31.16 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ]. % 30.96/31.16 apply (zenon_notor_s _ _ zenon_Ha4). zenon_intro zenon_Ha6. zenon_intro zenon_Ha5. % 30.96/31.16 apply zenon_Ha5. zenon_intro zenon_Ha7. % 30.96/31.16 elim (classic (zenon_TU_fj = zenon_TU_fj)); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ]. % 30.96/31.16 cut ((zenon_TU_fj = zenon_TU_fj) = ((nil) = zenon_TU_fj)). % 30.96/31.16 intro zenon_D_pnotp. % 30.96/31.16 apply zenon_Ha0. % 30.96/31.16 rewrite <- zenon_D_pnotp. % 30.96/31.16 exact zenon_Ha8. % 30.96/31.16 cut ((zenon_TU_fj = zenon_TU_fj)); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 30.96/31.16 cut ((zenon_TU_fj = (nil))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 30.96/31.16 congruence. % 30.96/31.16 cut ((zenon_TU_fj = zenon_TW_ei) = (zenon_TU_fj = (nil))). % 30.96/31.16 intro zenon_D_pnotp. % 30.96/31.16 apply zenon_Haa. % 30.96/31.16 rewrite <- zenon_D_pnotp. % 30.96/31.16 exact zenon_Ha1. % 30.96/31.16 cut ((zenon_TW_ei = (nil))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 30.96/31.16 cut ((zenon_TU_fj = zenon_TU_fj)); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 30.96/31.16 congruence. % 30.96/31.16 apply zenon_Ha9. apply refl_equal. % 30.96/31.16 apply zenon_Hab. apply sym_equal. exact zenon_Ha7. % 30.96/31.16 apply zenon_Ha9. apply refl_equal. % 30.96/31.16 apply zenon_Ha9. apply refl_equal. % 30.96/31.16 apply (zenon_notor_s _ _ zenon_Ha3). zenon_intro zenon_Had. zenon_intro zenon_Hac. % 30.96/31.16 apply zenon_Hac. zenon_intro zenon_H77. % 30.96/31.16 elim (classic (zenon_TU_fj = zenon_TU_fj)); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ]. % 30.96/31.16 cut ((zenon_TU_fj = zenon_TU_fj) = ((nil) = zenon_TU_fj)). % 30.96/31.17 intro zenon_D_pnotp. % 30.96/31.17 apply zenon_Ha0. % 30.96/31.17 rewrite <- zenon_D_pnotp. % 30.96/31.17 exact zenon_Ha8. % 30.96/31.17 cut ((zenon_TU_fj = zenon_TU_fj)); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 30.96/31.17 cut ((zenon_TU_fj = (nil))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 30.96/31.17 congruence. % 30.96/31.17 cut ((zenon_TU_fj = zenon_TW_ei) = (zenon_TU_fj = (nil))). % 30.96/31.17 intro zenon_D_pnotp. % 30.96/31.17 apply zenon_Haa. % 30.96/31.17 rewrite <- zenon_D_pnotp. % 30.96/31.17 exact zenon_Ha1. % 30.96/31.17 cut ((zenon_TW_ei = (nil))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 30.96/31.17 cut ((zenon_TU_fj = zenon_TU_fj)); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 30.96/31.17 congruence. % 30.96/31.17 apply zenon_Ha9. apply refl_equal. % 30.96/31.17 generalize (ax41 zenon_TW_ei). zenon_intro zenon_Hae. % 30.96/31.17 apply (zenon_imply_s _ _ zenon_Hae); [ zenon_intro zenon_H7f | zenon_intro zenon_H74 ]. % 30.96/31.17 exact (zenon_H7f zenon_H75). % 30.96/31.17 elim (classic ((nil) = (nil))); [ zenon_intro zenon_Haf | zenon_intro zenon_H60 ]. % 30.96/31.17 cut (((nil) = (nil)) = (zenon_TW_ei = (nil))). % 30.96/31.17 intro zenon_D_pnotp. % 30.96/31.17 apply zenon_Hab. % 30.96/31.17 rewrite <- zenon_D_pnotp. % 30.96/31.17 exact zenon_Haf. % 30.96/31.17 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 30.96/31.17 cut (((nil) = zenon_TW_ei)); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 30.96/31.17 congruence. % 30.96/31.17 cut (((nil) = zenon_TV_ej) = ((nil) = zenon_TW_ei)). % 30.96/31.17 intro zenon_D_pnotp. % 30.96/31.17 apply zenon_Hb0. % 30.96/31.17 rewrite <- zenon_D_pnotp. % 30.96/31.17 exact zenon_Ha2. % 30.96/31.17 cut ((zenon_TV_ej = zenon_TW_ei)); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 30.96/31.17 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 30.96/31.17 congruence. % 30.96/31.17 apply zenon_H60. apply refl_equal. % 30.96/31.17 generalize (ax41 zenon_TX_dv). zenon_intro zenon_Hb1. % 30.96/31.17 apply (zenon_imply_s _ _ zenon_Hb1); [ zenon_intro zenon_H66 | zenon_intro zenon_Hb2 ]. % 30.96/31.17 exact (zenon_H66 zenon_H61). % 30.96/31.17 generalize (zenon_Hb2 (nil)). zenon_intro zenon_Hb3. % 30.96/31.17 apply (zenon_imply_s _ _ zenon_Hb3); [ zenon_intro zenon_H82 | zenon_intro zenon_Hb4 ]. % 30.96/31.17 exact (zenon_H82 ax17). % 30.96/31.17 apply (zenon_imply_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H76 ]. % 30.96/31.17 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_H62 | zenon_intro zenon_H67 ]. % 30.96/31.17 apply (zenon_L2_ zenon_TX_dv); trivial. % 30.96/31.17 generalize (ax52 zenon_TX_dv). zenon_intro zenon_Hb6. % 30.96/31.17 apply (zenon_imply_s _ _ zenon_Hb6); [ zenon_intro zenon_H66 | zenon_intro zenon_Hb7 ]. % 30.96/31.17 exact (zenon_H66 zenon_H61). % 30.96/31.17 apply (zenon_equiv_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb9; zenon_intro zenon_H6c | zenon_intro zenon_Hb8; zenon_intro zenon_H68 ]. % 30.96/31.17 cut (((nil) = zenon_TV_ej) = ((nil) = zenon_TX_dv)). % 30.96/31.17 intro zenon_D_pnotp. % 30.96/31.17 apply zenon_H6c. % 30.96/31.17 rewrite <- zenon_D_pnotp. % 30.96/31.17 exact zenon_Ha2. % 30.96/31.17 cut ((zenon_TV_ej = zenon_TX_dv)); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 30.96/31.17 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 30.96/31.17 congruence. % 30.96/31.17 apply zenon_H60. apply refl_equal. % 30.96/31.17 exact (zenon_Hba zenon_H6e). % 30.96/31.17 apply (zenon_L3_ zenon_TX_dv); trivial. % 30.96/31.17 apply (zenon_L5_ zenon_TV_ej zenon_TX_dv zenon_TW_ei); trivial. % 30.96/31.17 apply zenon_H60. apply refl_equal. % 30.96/31.17 apply zenon_H60. apply refl_equal. % 30.96/31.17 apply zenon_Ha9. apply refl_equal. % 30.96/31.17 apply zenon_Ha9. apply refl_equal. % 30.96/31.17 Qed. % 30.96/31.17 % SZS output end Proof % 30.96/31.17 (* END-PROOF *) % 30.96/31.17 nodes searched: 382357 % 30.96/31.17 max branch formulas: 15419 % 30.96/31.17 proof nodes created: 33303 % 30.96/31.17 formulas created: 1842617 % 30.96/31.17 %------------------------------------------------------------------------------